"straight edge drinking game" is a humorous expression that implies that a certain event or series of events will not happen, or will happen with very little regularity.
It's equivalent to saying "that will never happen", "no chance". "not in a million years" or other idiomatic expressions.
Example 1:
Joe: Hey, let's drink every time Bush says something smart.
Nick: That's a straight edge drinking game.
Example 2:
Andre: Here's a straight edge drinking game. Let's drink whenever Charles Bronson goes 5 minutes without killing somebody.
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